lightdm: Is one or another screen administrator really linked to DE?

Several articles say that most DM GUIs are used for a particular DE, for example, GDM is for GNOME, LXDM – LXDE, etc. And only LightDM is described as a "cross-desk" DM. I'm sure that does not mean that they can only be used with the related DE, but I ask them beforehand: does something change? Can I consider getting something else, except GDM, for a new Linux distribution?